2.3 Sequences

• The common difference in an arithmetic sequence can only be positive.

  False
• What is the constant value called in a geometric sequence?

  Common ratio
• Unlike arithmetic sequences, geometric sequences use multiplication
• Match the variable in the arithmetic sequence formula with its meaning:

  $a_{n}$ ↔️ nth term

  $a_{1}$ ↔️ First term

  $n$ ↔️ Term number

  $d$ ↔️ Common difference
• The term number $n$ in the arithmetic sequence formula refers to the position of the term in the sequence.


  True
• What does $a_{n}$ represent in the formula for the nth term of an arithmetic sequence?


  The nth term
• After substituting the values into the formula, you must evaluate the expression
• In the sequence 3, 7, 11, 15, 19, ..., the common difference $d$ is 4
• What is the constant value added to each term in an arithmetic sequence called?

  Common difference
• In an arithmetic sequence, each term is found by adding the common difference to the previous term.
• Arithmetic sequences use multiplication to generate the next term.

  False
• What are the possible values of the common ratio *r* in a geometric sequence?

  Positive, negative, or zero
• Geometric sequences use addition to find the next term.

  False
• The nth term of an arithmetic sequence is given by the formula: $a_{n} =$$a_{1} +$$(n - 1)d$
• What are the two primary values needed to find the nth term of an arithmetic sequence?

  First term and common difference
• The formula to find the nth term of a geometric sequence is a_{1}
• Arithmetic sequences use addition, while geometric sequences use multiplication to find the nth term.


  True
• The constant value added in an arithmetic sequence is called the common difference.
• What is the constant value added in an arithmetic sequence called?

  Common difference
• An arithmetic sequence can only be increasing

  False
• In a geometric sequence, each term is obtained by multiplying the previous term by a constant value called the common ratio
• What are the possible values of the common ratio in a geometric sequence?

  Positive, negative, or zero
• Match the sequence type with its method of generating the next term:

  Arithmetic ↔️ Addition

  Geometric ↔️ Multiplication
• What is the 7th term in the arithmetic sequence 3, 7, 11, 15, 19, ...?

  27
• The formula to find the $n^{th}$ term in a geometric sequence is a_{n} = a_{1} \cdot r^{n - 1}
• What is the 5th term in the geometric sequence 2, 6, 18, 54, ...?

  162
• What is the formula to find the $n^{th}$ term in a geometric sequence?


  $a_{n} =$$a_{1} \cdot r^{n - 1}$
• What does $r$ represent in the formula $a_{n} =$$a_{1} \cdot r^{n - 1}$?


  Common ratio
• What is the first term in the geometric sequence 2, 6, 18, 54, ...?

  2
• Arithmetic sequences use multiplication to find the next term, while geometric sequences use addition.

  False
• In the arithmetic sequence formula $a_{n} =$$a_{1} +$$(n - 1)d$, $d$ represents the common difference.
• Steps to find the $n^{th}$ term in an arithmetic sequence:


  1️⃣ Identify the first term (a_{1}</latex>)

  2️⃣ Calculate the common difference ($d$)

  3️⃣ Determine the term number ($n$)

  4️⃣ Substitute into the formula $a_{n} =$$a_{1} +$$(n - 1)d$
• The formula $a_{n} =$$a_{1} \cdot r^{n - 1}$ is used to find the $n^{th}$ term in an arithmetic sequence.


  False
• What is the formula to find the nth term in a geometric sequence?

  $a_{n} =$$a_{1} \cdot r^{n - 1}$
• In the geometric sequence 2, 6, 18, 54, 162, the common ratio is 3.


  True
• What is the formula to find the nth term in an arithmetic sequence?

  a_{n} = a_{1} + (n - 1)d</latex>
• In the arithmetic sequence 3, 7, 11, 15, 19, the common difference is 4.


  True
• In an arithmetic sequence, each term is obtained by adding a constant value called the common difference
• Unlike geometric sequences, arithmetic sequences use addition
• Each term in a geometric sequence is found by multiplying the previous term by the common ratio.

  True